Floquet topological insulators (FTIs) have been used to study the topological features of a dynamic quantum system within the band structure. However, it is difficult to directly observe the dynamic modulation of band structures in FTIs. Here, we implement the dynamic Su–Schrieffer–Heeger model in periodically curved waveguides to explore new behaviors in FTIs using light field evolutions. Changing the driving frequency produces near-field evolutions of light in the high-frequency curved waveguide array that are equivalent to the behaviors in straight arrays. Furthermore, at modest driving frequencies, the field evolutions in the system show boundary propagation, which are related to topological edge modes. Finally, we believe curved waveguides enable profound possibilities for the further development of Floquet engineering in periodically driven systems, which ranges from condensed matter physics to photonics.